JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 107, NO. B12, 2380, doi:10.1029/2001JB000713, 2002 Joint inversion of normal mode and body wave data for inner core anisotropy 2. Possible complexities Miaki Ishii and Adam M. Dziewon´ski Department of Earth and Planetary Sciences, Harvard University, Cambridge, Massachusetts, USA Jeroen Tromp Seismological Laboratory, California Institute of Technology, Pasadena, California, USA Go¨ran Ekstro¨m Department of Earth and Planetary Sciences, Harvard University, Cambridge, Massachusetts, USA Received 19 June 2001; revised 10 June 2002; accepted 8 July 2002; published 31 December 2002. [1] In this study we focus on inner core sensitive body wave data to investigate lateral and radial heterogeneity within the inner core. Normal mode data are used to constrain a global model and to monitor if complexities introduced by body wave data are compatible with mode measurements. In particular, we investigate the possibilities of an isotropic layer near the inner core boundary and large-scale variations in anisotropy such as hemispheric dependence proposed in studies based upon differential travel time data. Travel time data from distances between 130° and 140° require anisotropy near the inner core boundary. This evidence is supported by differential travel time data based upon diffracted waves, contrasting the previous inferences of isotropy at the surface of the inner core. Our experiments also show that variations at a hemispheric scale are not necessary and that the sources of apparent hemispheric differences can be localized. A comparison of differential and absolute travel time data suggests that differences in inferred inner core anisotropy models arise mainly from a few anomalous paths. These paths are responsible for the strong anisotropy which is characteristic of models based upon differential data. Assuming constant anisotropy in the inner core, we investigate the distribution of residual differential travel times at the entry and exit points of rays turning within the outer core. The results are consistent with existing models of structure near the core-mantle boundary. Placing the source of the difference between differential and absolute travel time data in the lowermost mantle gives a more satisfactory result than attempting to model it with a complex inner core. INDEX TERMS: 7207 Seismology: Core and mantle; 7260 Seismology: Theory and modeling; 7203 Seismology: Body wave propagation; 7255 Seismology: Surface waves and free oscillations; KEYWORDS: inner core, anisotropy, PKIKP, differential travel times, hemispheric variations Citation: Ishii, M., A. M. Dziewon´ski, J. Tromp, and G. Ekstro¨m, Joint inversion of normal mode and body wave data for inner core anisotropy, 2, Possible complexities, J. Geophys. Res., 107(B12), 2380, doi:10.1029/2001JB000713, 2002. 1. Introduction differential travel time data is the similarity of the mantle ray path of waves turning in the outer core (BC or AB) and the [2] The properties of the Earth’s inner core have been inner core (DF) (Figure 1). This similarity allows one to investigated using three different types of data: normal modes assume that differential measurements do not include effects [e.g., Woodhouse et al., 1986; Tromp,1993;Durek and due to the source, receiver, or mantle, and hence that the Romanowicz, 1999], absolute travel times of PKIKP (or travel time anomalies are solely due to the path within the PKP ) [e.g., Morelli et al., 1986; Shearer et al., 1988; DF inner core. Many models of the inner core have been Su and Dziewon´ski, 1995], and the differential travel proposed using differential travel time data, some of which times BC DF (or PKP PKP )andAB DF (or À BCÀ DF À contain structures not seen in models based upon other types PKP PKP ) [e.g., Creager, 1992; Song and Helmberger, ABÀ DF of data, such as an isotropic layer near the inner core 1993; Vinnik et al., 1994; McSweeney et al., 1997; Tanaka boundary [e.g., Song and Helmberger, 1998], a transition and Hamaguchi, 1997]. The advantage of the high-quality zone within the inner core [e.g., Song and Helmberger, 1998], and hemispherically dependent anisotropy [e.g., Copyright 2002 by the American Geophysical Union. Tanaka and Hamaguchi, 1997; Creager, 1999; Niu and 0148-0227/02/2001JB000713$09.00 Wen, 2001]. ESE 21 - 1 ESE 21 - 2 ISHII ET AL.: JOINT INVERSION FOR IC ANISOTROPY, 2 Figure 1. (left) Ray paths for AB, BC, and DF at an epicentral distance range of 150°, and (right) a travel time table for PKP branch using PREM [Dziewon´ski and Anderson, 1981]. For the travel time table we use an earthquake with a source depth of 300 km. [3] In the companion paper (Ishii et al. [2002], hereinafter Vinnik et al., 1994; Song, 1996; McSweeney et al., 1997], referred to as paper 1), we demonstrate that it is relatively whereas absolute travel times tend to result in models with easy to obtain a simple anisotropic inner core model which weaker anisotropy [e.g., Su and Dziewon´ski, 1995]. To fits all three types of data. Normal mode and mantle- investigate this discrepancy, we compare absolute and corrected DF data are compatible with one another and differential travel time data. Contamination of differential good fits can be achieved using a constant anisotropy data due to mantle structure near the core-mantle boundary model. Differential travel time data are harder to fit. In this (CMB) has also been suggested [e.g., Breger et al., 1999, paper we explore the source of this difficulty by (1) 2000], especially for the AB rays. We follow this suggestion considering in detail paths sampled by differential data; and investigate if the residual differential travel time signal (2) introducing structure within the inner core; and (3) based upon a constant anisotropy model can be placed in the investigating the possible effects of D" heterogeneity. Our mantle. focus is on large-scale structure, and therefore the existence of lateral variations [e.g., Su and Dziewon´ski, 1995], except for hemispheric variations or small-scale structure [e.g., 2. Comparison of Body Wave Data Creager, 1997; Dziewon´ski, 2000; Vidale and Earle, [6] We use normal mode splitting functions [He and 2000], is addressed only briefly. We assume that the Tromp, 1996; Resovsky and Ritzwoller, 1998; Durek and symmetry axis of the inner core is aligned with the rotation Romanowicz, 1999], ISC DF residuals, and high-quality axis, and we do not consider differential rotation [e.g., differential travel time data [Creager, 1992; Vinnik et al., Shearer and Toy, 1991; Creager, 1992; Song and Richards, 1994; McSweeney, 1995; Song, 1996; Creager, 1997; 1996; Su et al., 1996; Souriau and Poupinet, 2000] in our McSweeney et al., 1997; Tanaka and Hamaguchi, 1997; analysis. A detailed discussion of the theory, data, and Creager, 1999] to investigate the structure of the inner core. inversion method used in this paper can be found in paper 1. Before using these data, we explore the differences between [4] Using all available data, we investigate if the intro- mantle-corrected absolute and differential travel time data. duction of an isotropic layer near the inner core boundary For details of data processing, see paper 1. If the mantle (ICB) can improve the fit, especially to differential travel correction to absolute and differential travel times is appro- time data [e.g., Song and Helmberger, 1995; Creager, priate, these two sets of data should agree well. The fact that 2000]. We also explore the possibility of hemispherically models obtained from independent inversions of these two distinct anisotropy, previously proposed on the basis of data sets differ significantly suggest that this is not the case. body wave measurements [e.g., Tanaka and Hamaguchi, [7] The BC arrivals are observed in the 145° to 153° 1997; Creager, 1999; Niu and Wen, 2001]. Normal modes epicentral distance range (Figure 1), and the corresponding do not constrain this type of structure, because they are only BCÀDF data are sensitive to inner core structure down to sensitive to even-degree anomalies. Focusing on absolute roughly 300 km beneath the ICB. There are 851 BCÀDF body wave data, we investigate if large-scale variations, measurements in our data set, spanning the distance from including hemispheric variation, in inner core anisotropy 145° to 160°. Data with an epicentral distance greater than can be observed consistently. We use both normal mode and 153° involve diffracted BC traveling along the ICB. We body wave data to constrain the global average and consider discard these data when performing inversions but return to hemispheric deviations as perturbations from this average. them in section 4, where we consider structure near the ICB. [5] In general, inner core models derived using absolute The remaining 512 BCÀDF data are binned into two and differential travel time data differ most in their level of distance ranges, 145° to 150° and 150° to 153°,and anisotropy. Models based upon differential travel times have averaged for each 0.1 increment in cos2 x, where x is the strong anisotropy [e.g., Creager, 1992; Song and Helm- angle between the direction of wave propagation and the berger, 1993], especially near the center of the Earth [e.g., symmetry axis of transverse isotropy. The averaging process ISHII ET AL.: JOINT INVERSION FOR IC ANISOTROPY, 2 ESE 21 - 3 reduces the effects of mantle heterogeneity by cancelling out the isotropic signal if the outer core entry and exit positions of BC or AB cover the globe uniformly. In this paper we show that differential travel time data coverage is uneven compared to absolute travel time data, and suggest biased sampling as the reason for difference in inner core models derived from these two data sets. [8] We compare BCÀDF data in the range from 150° to 153° with DF from the same distance range (Figure 2a).